Let me begin by saying here that I haven't read any of the other responses, so please forgive me if I add anything terribly redundant. Likewise, these are, as always, just my own personal opinions.
To answer the OP's question directly, as a general rule, -NO-, I will NOT show people unedited images. There are VERY RARE exceptions...for a recent shoot, I did in fact provide the client with ALL the images from the shoot, however in this case "the client" was actually one of my former college professors...specifically one of my digital art professors, including my Photoshop teacher. In this very specific case, I did feel comfortable with the person seeing the "unfinished work", as I -know- said person not only has the experience and expertise to judge the work fairly (not to mention pick out some shots I may have over-looked), but I also wanted this particular person to have the option of editing the work if they choose. That said however, in MOST cases, they client will ONLY see the finished (or semi finished) images I provide. As with the days of film, depending on the commission, the contract, the number of prints requested, etc., I will usually provide the client with a "contact sheet"...a print out of various images that, at the very least have been processed thru Camera RAW with fairly basic adjustments. Once the client had decided which prints they want (whether the prints are physical, as with photo paper, or virtual, such as jpgs or pngs to use on a website), then I will put the finish on those images to provide for delivery.
As I've said elsewhere, in my mind photography is a process...what you do at the camera is only PART of that process. What I do in an image editing program after the image is shot is JUST AS IMPORTANT as what I did with the camera. It's NOT about making mistakes (NEVER tell the client you've shot multiple images because you "made a mistake"), it's about providing the client with the best options possible and in my mind, those options including image processing.
To use an example here, let's assume that I'm shooting a local "band". Let's say that said band has retained my services as they need some shots for either their website or even an album (CD) cover and the agreement was for me to provide 20 jpg images for said purpose (such details would ABSOLUTELY be included in the contract). When I go to their gig on the prearranged Saturday night, I may shoot as many as 80 to 100 pics OR MORE, depending on any specific shots they have requested (back stage shots? shots of the crowd? shots of the venue or marquis?) and depending on how long they have retained my services for (unless other specific arrangements have been made, I do typically charge BY THE HOUR). I will often allow the client to take a peek at a few select shots on the camera, if nothing else to put the client's mind at ease that they're getting their money's worth, however I do NOT usually tell the client how many shots I've taken in a given shoot. In my mind, even if I had to shoot 200 images to get those 20, it's irrelevant AS LONG as I'm able to provide those 20 shots (not that it should generally take that many shots, but you get the point). Once I feel I've gotten the needed shots and/or once the time clock has ticked down (LOL), I'll pack up my gear and head home. The next day (usually...give or take the confines of the contract), I sit down, weed out the bad shots, then do some rough initial adjustments (Camera RAW, perhaps a crop here and there, etc) to (hopefully) provide a contact sheet with 30 - 40 shots to choose from. FOR MYSELF this is important...even though the contract may be to provide only 20 prints, I've often found that by providing the client with some additional options, they may be willing to revise the contract and pony up some extra cash for a few more prints..in fact I'll often include such options in the contract itself ("additional 8x10 prints available for $20 each" or something to that effect). Once the client has selected the shots they want from the contact sheet, I will go ahead and put the finishing touches on said images, with any remainder of payment due on delivery (I will usually charge an up front fee for my services depending on the client and the job...$50 up front, with the remainder due on delivery). I do try to be as flexible as I can and obviously every situation and client is different, however that's pretty much my base modus operandi.
Now you should have noticed the repeated use of the word "contract". At the risk of being horribly blunt, if you're doing paid work for others and you're working without a contract, you're a complete fool! In the case of "One girl is particularly persistent with her "demanding" unedited photos...", you can simply pull out the contract and clearly show that no such stipulation was included in the contract THAT SHE SIGNED. While this obviously applies to MORE than just photography and while I'm sure it's going to sound terribly jaded, remember this one simple fact; PEOPLE SUCK! It's nice to believe that all people are good-natured and capable of doing business with little more than a "gentleman's handshake", unfortunately the reality is often quite the opposite....sooner or later you WILL run into clients who are demanding, if not totally unreasonable. You need to make it clear that unless it is otherwise specifically stipulated in the contract, that the client has no artistic say in how YOUR work is completed. You were hired to provide a service and the definition of that service should be clearly outlined in the contract. Consider this (and feel free to use it to illustrate the point to the girl in question); you wouldn't expect to walk into a JC Penny Portrait Studio and expect to have ANY creative control over how the images are processed. You go in (or take your kid in), you'll probably sign some form of contract or release, pose for the shots (just like a model) and pay at the cash register when you receive your prints. It's a business...period. Likewise a contract should also stipulate exactly HOW the images you shot are to be used, particularly regarding issues involving copyright and such. In nutshell legal definitions, unless otherwise stated in the contract, YOU retain ownership of the images shot. For example, if you shot a model and in a hypothetical situation, that model should become famous, you do NOT want to see your work used in a multi million dollar ad campaign up on billboards for Walmarts or something, if you only got a measly $50 for the image. "Royalties" should be an expected part of the business! Obviously this doesn't happen with the average client and but the POTENTIAL is there. Certainly there are business folk far better versed in all of this than I am (and obviously this is what a good lawyer is for as well), however the bottom line is this - ALWAYS cover your own ass!
In other words, whether or not you show your unfinished work to a given client usually depends on the conditions you set forth when your services are initially retained. In most cases, I don't advise it, however it's really up to you. Just make sure that both you and your clients are aware of any such conditions (preferably in writing) ahead of time so you don't end up with the proverbial can of worms.
Again, while again these are just my own personal opinions and I do hope they will be considered as such, in this case do keep in mind that I'm NOT a lawyer or legal counselor...when it doubt, consult your local bar association on such matters.